Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  int n;
  while (cin >> n) {
    int a, b;
    bool can = false;
    for (int i = 1; (i * (i + 1)) / 2 < n; ++i) {
      a = (i * (i + 1)) / 2;
      for (int j = i; (j * (j + 1)) / 2 < n; ++j) {
        b = (j * (j + 1)) / 2;
        if (a + b == n) {
          can = true;
          goto label;
        } else if (a + b > n)
          break;
      }
    }
  label:
    if (can)
      cout << "YES" << endl;
    else
      cout << "NO" << endl;
  }
  return 0;
}